For a, b belongs to R define xRy to mean that x-y belongs to Z. (1) Prove that Relation is an equivalence relation on R. (2) List three real numbers x such that x related to square root 2
Answer (1)
12th Nov, 2020
Hello Jitendra!
It is not possible to answer the question unless we know what set R is. So kindly give the value of elements in set R. In order to prove that the above relation of x-y is equivalence, it must be proved that x-y is reflexive, symmetric and transitive. By definition, a reflexive relation is one in follows that for every x that belongs to R, (x,x) must be true. A relation is called symmetric if (x,y) belongs to Z then, (y,x) must also belong to Z where Z is the set defined over the relation xRy. Similarly, the relation is transitive if (x,y),(y,z) belong to Z then (x,z) also belong to Z.
So, follow these rules of relations and check for set Z.
Comments (0)
